A070562 - OEIS

%I #12 Aug 28 2016 18:18:34

%S 0,10,9,9,8,1,8,7,7,6,0,8,7,7,6,1,6,6,5,3,0,5,5,4,5,2,4,5,2,3,0,3,4,2,

%T 2,1,3,3,3,2,0,4,1,2,1,3,1,2,1,4,0,5,3,8,2,1,4,2,2,1,0,2,2,5,5,2,1,1,

%U 7,5,0,4,4,2,1,1,6,5,3,2,0,4,2,1,7,3,3,3,4,3,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0

%N Fecundity of n.

%C Start with x=n, repeatedly replace x by x + product of digits of x until the product is 0; fecundity = number of steps. a(0) = 0 by convention.

%D P. Tougne, Jeux Mathematiques column, Pour La Science (French edition of "Scientific American"), Vol. 82, Aug. 1984, Prob. 6, pp. 101, 104.

%H T. D. Noe, <a href="/A070562/b070562.txt">Table of n, a(n) for n = 0..10000</a>

%e 1 -> 2 -> 4 -> 8 -> 16 -> 22 -> 26 -> 38 -> 62 -> 74 -> 102 has fecundity 10.

%t f[ n_ ] := Block[ {a=n,b,c=0}, While[ b=Times@@IntegerDigits[ a ]; b>0, a=a+b; c++ ]; c ]; f[ 0 ]=0; Table[ f[ n ], {n,0,100} ]

%t f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f, 105, 0] (* _Robert G. Wilson v_, Jun 27 2010 *)

%o (PARI) prodig(n) = local(s, d); if(n==0, s=0, s=1; while(n>0, d=divrem(n, 10); n=d[1 ]; s=s*d[2 ])); s for(n=0, 92, x=n; c=0; while((d=prodig(x))!=0, c++; x=x+d); print1(c, ", "))

%Y Cf. A070560. A070561, A031346, A003001, A070061, A070257.

%K nonn,easy,base

%O 0,2

%A _N. J. A. Sloane_, May 07 2002

%E Edited and extended by _Klaus Brockhaus_, May 08 2002

%E Clarified the definition of fecundity and improved the Mathematica program. - _T. D. Noe_, Oct 06 2008

%E More terms from _Robert G. Wilson v_, Jun 27 2010